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This work studies the problem of learning unbiased algorithms from biased feedback for recommendation. We address this problem from a novel distribution shift perspective. Recent works in unbiased recommendation have advanced the state-of-the-art with various techniques such as re-weighting, multi-task learning, and meta-learning. Despite their empirical successes, most of them lack theoretical guarantees, forming non-negligible gaps between theories and recent algorithms. In this paper, we propose a theoretical understanding of why existing unbiased learning objectives work for unbiased recommendation. We establish a close connection between unbiased recommendation and distribution shift, which shows that existing unbiased learning objectives implicitly align biased training and unbiased test distributions. Built upon this connection, we develop two generalization bounds for existing unbiased learning methods and analyze their learning behavior. Besides, as a result of the distribution shift, we further propose a principled framework, Adversarial Self-Training (AST), for unbiased recommendation. Extensive experiments on real-world and semi-synthetic datasets demonstrate the effectiveness of AST.